Construction of quantum Dirac observables and the emergence of WKB time
arXiv:1910.02998 · doi:10.1103/PhysRevD.101.086001
Abstract
We describe a method of construction of gauge-invariant operators (Dirac observables or ``evolving constants of motion'') from the knowledge of the eigenstates of the gauge generator in time-reparametrization invariant mechanical systems. These invariant operators evolve unitarily with respect to an arbitrarily chosen time variable. We emphasize that the dynamics is relational, both in the classical and quantum theories. In this framework, we show how the ``emergent Wentzel-Kramers-Brillouin time'' often employed in quantum cosmology arises from a weak-coupling expansion of invariant transition amplitudes, and we illustrate an example of singularity avoidance in a vacuum Bianchi I (Kasner) model.
arXiv commentv2: references updated, minor typos corrected, title slightly changed, conceptual clarifications added, published in Physical Review D
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